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340 Radio Engineering for Wireless Communication and Sensor Applications

Figure 12.22 Spectral line of ozone centered at 110.836 GHz (background noise of atmosphere removed) and height profile corresponding to this line.

Example 12.4

A ground surface having a temperature of 295K and an emissivity of 1 is covered with a quarter-wave layer of lossless material having a relative permittivity of 5. Find the antenna temperature measured with a radiometer pointing perpendicularly to the surface. Assume that the brightness temperature of sky is 0K.

Solution

 

 

 

 

 

 

 

 

Z layer =

 

=

 

/

 

=

The wave impedance of the layer is

m/e

m0 /e0

er

376.7/5 V = 168.5V. Because now the ground is like a blackbody (emissiv-

ity e =

1), its wave impedance Z ground = 376.7V equals the wave impedance

of free

space, h0 . The layer operates

as a quarter-wave transformer (see

Section 4.3.3) that transforms Z ground

to a value of Z t = Z layer2 /Z ground =

75.4V. The reflection coefficient between the free space and this impedance is r = (h 0 Z t ) / (h0 + Z t ) = 0.666. The brightness temperature of the ground is TB = eT = X1 | r | 2 CT = 164K. This is also the antenna temperature seen by the radiometer, because the lossless layer itself does not emit thermal radiation and the sky is cold. Without the layer, the antenna noise temperature would be 295K.

12.7.2 Total Power Radiometer and Dicke Radiometer

A radiometer is a sensitive receiver that measures absolute noise power levels accurately and that is calibrated to display the brightness temperature.

Figure 12.23 shows a block diagram of a total power radiometer. It is a superheterodyne receiver, whose IF signal is fed to a detector. The mixer

 

 

 

 

 

 

Applications

341

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 12.23 Total power radiometer.

usually converts both the upper and lower sideband to IF. The measurement bandwidth is determined by the noise bandwidth of the IF stage, Bn . The detected signal is integrated to average the noisy output voltage Vout , shown in Figure 12.24. The output voltage includes both dc and ac components. The dc component is directly proportional to the system noise temperature:

Vdc = GS (TA + TR )

(12.14)

The ac component, Vac , comes from the statistical nature of noise. The ratio of the rms value of Vac to the dc component Vdc is 1/Bn t [9, 12], where t is the integration time of the detector output voltage. The sensitivity of a radiometer is defined as the minimum change of the antenna

Figure 12.24 Output voltage of a total power radiometer.

342 Radio Engineering for Wireless Communication and Sensor Applications

noise temperature that can be detected. For a total power radiometer, the sensitivity is

DT =

TA + TR

(12.15)

Bn t

A change of DT at the input produces at the output a change equal to the rms value of Vac . The sensitivity can also be defined to be that change at the input that produces a change equal to the peak-to-peak value of the output voltage, Vpp . The peak-to-peak value is about six times the rms value.

The variations of the system gain, GS , reduce the accuracy of a measurement. The gains of the amplifiers, mixer, and detector may depend on temperature and supply voltages. The effect of slow variations can be taken into account by calibrating the radiometer frequently with loads having known brightness temperatures. Rapid gain fluctuations deteriorate the sensitivity of the total power radiometer:

DT = (TA + TR ) 1t + SDGS D2 (12.16)

Bn GS

where DGS is the rms value of the gain fluctuations. However, tight temperature control of the radiometer components successfully mitigates these problems.

Figure 12.25 shows the block diagram of the Dicke radiometer, in which the influence of gain variations is reduced. The receiver switches continuously between the antenna and a noise source that has a constant

Figure 12.25 Dicke radiometer.

Applications

343

temperature, TC . Gain variations are assumed to be small between switching. The output of the diode is detected synchronously with the switch generator so that the output voltage, Vout , is proportional to the difference between TA and TC . If the radiometer is balanced, that is, TA = TC , gain variations have no influence on the output. A Dicke radiometer may be balanced by injecting excess noise into the antenna branch (usually TA < TC ), by changing the IF gain synchronously with a switch generator, or by adjusting the temperature TC . Because only half of the time is used for an effective measurement, the sensitivity, DT, of the Dicke radiometer is twice of that of the total power radiometer:

D = 2(TA + TR )

T (12.17)

Bn t

Example 12.5

A Dicke radiometer has a noise temperature TR = 500K and a bandwidth Bn = 10 MHz. A blackbody having a temperature of 300K should be measured with a resolution of 0.2K. Find the required integration time.

Solution

The system noise temperature TS = TA + TR = 800K. To obtain a sensitivity DT = 0.2K, we solve for the required integration time from (12.17) as t = (2TS /DT )2/Bn = (2 × 800/0.2)2/107 seconds = 6.4 seconds.

12.7.3 Remote-Sensing Radar

Side-looking airborne radar (SLAR), synthetic-aperture radar (SAR), scatterometer, and altimeter are radars used for remote sensing.

SLAR is pulse radar that is usually placed on an airplane. It produces microwave images of ground at the side of the flight track. The beam of the antenna is broad in the vertical direction and narrow in the horizontal direction, as shown in Figure 12.26. If the plane flies at an altitude of 5 km, for example, the image may cover a range from 4 km to 15 km at the side of the track. The resolution in the direction perpendicular to the flight track depends on the pulse length t as

DR r =

ct

(12.18)

2 sin u

 

 

where u is the angle of incidence. Thus, directly below the flight track at small u angles the resolution is bad. In the direction along the flight track,

344 Radio Engineering for Wireless Communication and Sensor Applications

Figure 12.26 SLAR.

the resolution depends on the beamwidth of the antenna. If the dimension of the antenna is D in the horizontal direction, the beamwidth is about l/D and the along-track or cross-range resolution at a distance of R is

DR cr =

Rl

(12.19)

D

 

 

The cross-range resolution gets worse as R increases and, therefore, SLAR onboard a satellite would need a very large antenna to obtain good resolution.

To overcome the limited cross-range resolution of SLAR, satellite remote-sensing radar is based on the principle of a synthetic aperture. Syn- thetic-aperture radar is pulse radar that uses the motion of the satellite (or some other vehicle) to synthesize the effect of a large antenna aperture. Echoes of several pulses are processed coherently to produce high-resolution images. If the pulses transmitted over a section of flight track having a length of s are processed, the resolution of this synthetic aperture equals that of an antenna having a width of 2s . Because a single-point target is in the view of the real antenna over a track section s Rl/D, the theoretical beamwidth of the synthetic-aperture radar is

us =

l

=

D

(12.20)

2s

2R